1. Field of the Invention
The present invention relates to an aspherical ophthalmic lens, and in particular, to the surface shape of the first surface of such a lens that has a positive refractive power.
2. Background of Related Art
Spherical surfaces are conventionally used on the first refractive surface (the surface on the side of the lens opposite the eye, i.e., the front refractive surface) of ophthalmic lenses that are used to correct refractive errors of the eye. A spherical surface is used because it is easy to manufacture. On the second refractive surface (the surface on the same side as the eye, i.e., the rear refractive surface), toric surfaces, as well as spherical surfaces, are used to correct astigmatism and other refractive errors. Hereinafter, a lens on which a spherical surface is used as the first surface will be referred to as a spherical lens, and a lens on which an aspherical surface is used as the first surface will be referred to as an aspherical lens.
Generally, the refractive power of a lens is expressed in units of diopters (D). The refractive power at the lens surface (the surface refractive power SRP) is defined in terms of the surface curvature .rho. (in units of m.sup.-1), the radius of curvature R (where R=1/.rho.) and the refractive index n of the lens material as EQU SRP(D)=(n-1).times..rho.=(n-1/R).
The refractive power of the first surface of the lens is hereinafter referred to specifically as the base curve. The curvature corresponding to the base curve is hereinafter referred to as the base curve curvature.
The refractive power of the lens is primarily determined by the refractive powers of the first and second refractive surfaces. Therefore, various values of the base curve can be used to obtain a desired lens refractive power, depending upon how the two surface refractive powers are combined. In practice, however, the base curve is limited to a characteristic range for the refractive power of the lens. By using a characteristic base curve, optical performance is ameliorated because the astigmatic aberration effect on the eye that results from viewing objects through sides of the lens that are spaced from the optical axis is reduced.
Generally, the known solution for minimizing the astigmatic aberration of an ophthalmic lens is referred to as Tscherning's ellipse. Tscherning's ellipse provides a hypothetical solution to the problem for a thin lens. In an actual lens, because the design accounts for the actual path of the light rays (i.e., the so-called ray trace) due to the center thickness of the lens, the actual solution is slightly different from the hypothetical solution. Nevertheless, the hypothetical solution provides an accurate approximation of the actual solution.
According to Tscherning's ellipse, the optimum base curve to minimize astigmatic aberration differs for far-range viewing and close-range viewing. In other words, the optimum base curve differs according to whether the lens is designed for far-range or close-range viewing. When far-range viewing and close-range viewing are equally emphasized (i.e., given the same weight in the calculations), values of the required base curve can be interpolated from the far-range vision base curve values and the close-range vision base curve values.
As a result, three conceivable designs exist, depending upon whether far-range viewing, close-range viewing or both are considered important. For the present invention, a design for far-range viewing and a design for close-range viewing will be described. A design that accounts for far- and close-range viewing equally, however, can be determined by those of ordinary skill in the art as a variant of these two designs.
The primary disadvantage arising from using lenses having a positive refractive power to correct for presbyopia and hypermetropia is that as the refractive power becomes stronger, the center thickness increases. Because large curvatures have to be used, the convex protrusion becomes more pronounced and detracts from the appearance of the lens.
In addition, as the lens curvature and refractive power increase, the image magnification ratio with respect to the retina of the eye also increases. Generally, the image magnification ratio M due to an ophthalmic lens is given by the following expression: EQU M={1/(1-d1*L)}*{1/(1-d*L1/n)}
In this expression, d1 is the distance along the optical axis between the entrance pupil and the rear vertex of the lens (in units of m), L is the rear vertex power of the lens (in units of D), d is the thickness of the center of the lens (in units of m), n is the refractive index of the lens and L1 is the refractive power of the first surface of the lens (in units of D). The first bracketed expression is the dioptric factor and the second bracketed expression is the shape factor.
FIG. 5 shows a lens surface shape of a conventional spherical surface lens that has been designed for far-range viewing (infinitely far). The refractive power of the lens in the Fig. is 4.0 D, and the lens diameter is 70 mm. This lens is a commonly used plastic lens with an refractive index of 1.50. The base curve is 9.0 D, and the edge thickness is 1.0 mm. The lens center thickness d is 6.6 mm, and the convex surface of the lens protrudes by 13.4 mm. As a result, the lens is very thick and unattractive. In this example, the radius of curvature R1 of the first side (the surface to the left of the drawing) is 55.555 mm, the radius of curvature R2 of the second surface (the surface to the right of the drawing) is 93.111 mm and the image magnification ratio M is 1.157. In other words, the image magnification ratio is 15.7%. As is known, the center thickness and the amount by which the lens protrudes can be reduced by decreasing the base curve.
FIG. 6 shows the lens surface shape of a lens with the same refractive power as that shown in FIG. 5 (4.0 D) with a base curve of 4.5 D. In this example, the lens center thickness is 5.9 mm, which is 0.7 mm thinner than the lens of FIG. 5. In addition, the protrusion amount is 6.7 mm, which is about half the protrusion amount of the lens of FIG. 5. In this example, the radius of curvature R1 of the first side is 111.111 mm, the radius of curvature R2 of the second side is 859.631 mm and the image magnification ratio M is 1.131. In other words, the image magnification ratio is 13.1%.
As one result of reducing the base curve, the image magnification ratio of the lens of FIG. 6 is smaller than that of the lens in FIG. 5. As another result of reducing the base curve, the shape factor of the lens of FIG. 6 decreases. As the refractive power increases due to the decreasing base curve, the effects of decreasing the image magnification ratio and decreasing the shape factor become more evident. Because the base curve itself is established from the standpoint of optical performance, however, the low base curve value of 4.5 D in this example results in poor optical performance.
FIGS. 7 and 8 show astigmatism in the field of view when lenses having base curves of 9.0 D and 4.5 D, respectively, are used. The vertical axis shows the angle of the field of view (units of .degree.), and the horizontal axis shows the astigmatism (units of D, the difference (m-s) between the meridional direction (m) and the sagittal direction (s)) taking the refractive power on the optical axis as the standard.
As shown in FIG. 7, in the lens with the base curve of 9.0 D, the astigmatism is desirably reduced over virtually the entire field of vision. Conversely, as shown in FIG. 8, in the lens with the base curve of 4.5 D, the astigmatism increases significantly toward the periphery of the field of vision. Therefore, FIGS. 7 and 8 show how selecting a base curve affects the final optical performance.
FIG. 9 shows the lens surface shape of a conventional spherical surface ophthalmic lens that is based on the close-range (30 cm) design. The refractive power of the ophthalmic lens shown is 4.0 D, and the lens diameter is 70 mm. This lens is a commonly used plastic lens with a refractive index of 1.50. The base curve is 7.0 D, and the lens edge thickness is 1.0 mm. In the case of this conventional example, the lens center thickness d is 6.2 mm, and the amount by which the convex surface protrudes is 10.2 mm. Although the protrusion amount is smaller than that of the lens designed for far-range viewing, the lens is thick and unattractive. In this example, the radius of curvature R1 of the first side is 71.429 mm, the radius of curvature R2 of the second side is 155.866 mm, and the image magnification ratio M is 1.144. In other words, the image magnification ratio becomes 14.4%. As discussed above in connection with the lens of FIG. 5, the base curve can be reduced to decrease the center thickness, the amount by which the lens protrudes and the image magnification ratio.
FIG. 10 shows the surface shape of a lens that has the same refractive power as the lens of FIG. 9 (4.0 D) and a base curve of 4.25 D. In this example, the lens center thickness is 5.9 mm, which is 0.3 mm thinner than the lens of FIG. 9. The amount by which the lens protrudes is 6.3 mm, which is 3.9 mm less than the protrusion amount of the lens of FIG. 9. In this example, the radius of curvature R1 of the first side is 117.647 mm, the radius of curvature R2 of the second side is 1549.776 mm and the image magnification ratio M is 1.130. In other words, the image magnification ratio is 13.0%.
As one result of reducing the base curve, the image magnification ratio of the lens of FIG. 10 is smaller than that of the lens in FIG. 9. As another result of reducing the base curve, the shape factor of the lens of FIG. 10 decreases. As the refractive power increases due to the decreasing base curve, the effects of decreasing the image magnification ratio and decreasing the shape factor become more evident. Because the base curve itself is established from the standpoint of optical performance, however, the low base curve value of 4.25 D in this example results in poor optical performance.
FIGS. 11 and 12 show astigmatism in the field of vision when lenses of 7.0 D and 4.25 D, respectively, are used. As shown in FIG. 11, in the lens with the base curve of 7.0, the astigmatism is desirably reduced over virtually the entire field of vision. Conversely, as shown in FIG. 12, in the lens with the base curve of 4.25 D, the astigmatism increases significantly toward the periphery of the field of vision.
Several methods exist for addressing the undesirable external appearance and reduced optical performance of a lens with a positive refractive power. These methods require using an aspherical surface as the first refractive surface. Examples of such aspherical lenses include Japanese Laid-open Patent Applications 52-136644 and 2-289818 and U.S. Pat. No. 4,504,128.
In the aspherical lens of Japanese Patent Application 52-136644, the aspherical lens includes quadratic lines, such as elliptical, parabolic, and hyperbolic lines, as the meridional line. By rotating these quadratic lines, the aspherical first refractive surface of the lens is formed. At present, this is the most common type of aspherical lens.
In the aphakia eye aspherical lens disclosed in U.S. Pat. No. 4,504,128, the aspherical surface is defined by an exponential function relating to the radius r, which is based on quadratic lines.
The common disadvantage of the lenses described above is that the curvature of the meridian line decreases rapidly and nearly monotonically from the center of the lens toward the periphery. As a result, the refractive power of the lens in the region adjacent the periphery is lower than the refractive power in the center region, and therefore, the effective field of vision from the standpoint of the user is reduced. In the case of aphakia eye ophthalmic lenses in particular, because a high refractive power aspherical surface is used, the effective field of vision decreases undesirably to a range of approximately 30 mm to at most 40 mm.
Similarly, the aspherical lens disclosed in Japanese Patent Application 2-289818 aims to achieve both high optical performance and a desirable external appearance. However, although the aspherical lens obtains a somewhat suitable result, the optical performance is still not sufficient.